Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in PYTHON3):

Solution:
# coding: utf-8
import queue
n,m,s,t=map(int,input().split())
table=[[] for i in range(n)]
inf=300001
dist_s=[inf for i in range(n)]
dist_t=[inf for i in range(n)]
s_list=[0 for i in range(inf+1)]
t_list=[0 for i in range(inf+1)]
s-=1;t-=1
for i in range(m):
    a,b=map(int,input().split())
    a-=1;b-=1
    table[a].append(b)
    table[b].append(a)
dist_s[s]=0
q=queue.Queue()
q.put(s)
while not q.empty():
    p=q.get()
    for e in table[p]:
        if dist_s[e]>dist_s[p]+1:
            dist_s[e]=dist_s[p]+1
            q.put(e)
dist_t[t]=0
q=queue.Queue()
q.put(t)
while not q.empty():
    p=q.get()
    for e in table[p]:
        if dist_t[e]>dist_t[p]+1:
            dist_t[e]=dist_t[p]+1
            q.put(e)
for i in range(n):
    s_list[dist_s[i]]+=1
    t_list[dist_t[i]]+=1
mindist=dist_s[t]
ans=0
for i in range(mindist-1):
    ans+=s_list[i]*t_list[(mindist-2)-i]
print(ans)